: The _____________ can be identified by looking at the dexterity that can be calculated using the Jacobian and the Inverse Jacobian when the matrix is non-singular.

The manipulability of a robot can be identified by looking at the dexterity that can be calculated using the Jacobian and the Inverse Jacobian when the matrix is non-singular.

Here are the steps to identify it:

1. Calculate the Jacobian: The Jacobian matrix provides a linear approximation of the function that describes the robot arm's configuration. It is a matrix of all first-order partial derivatives of a vector-valued function.

2. Calculate the Inverse Jacobian: If the Jacobian matrix is non-singular, we can calculate its inverse. The Inverse Jacobian is used when we know the desired speed of the end effector and we want to compute the required joint speeds to achieve it.

3. Calculate the dexterity: The dexterity (or manipulability) is a measure of how easy it is to move the robot arm in different directions. It can be calculated from the Jacobian. If the Jacobian has full rank (i.e., it is non-singular), then the robot arm is said to be well-conditioned, which means it can move with good dexterity.

4. Identify the manipulability: By looking at the dexterity calculated from the Jacobian and its inverse, we can identify the manipulability of the robot. High dexterity means high manipulability, and vice versa.